To a large extent we follow the original approach of Birman-Solomyak [1]}, which we recast in the framework of [2]}. However, our ultimate result (Theorem REF ) seems to be new, at least at the level of generality it is stated. In particular, it can be applied to
Schrödinger operators \(\Delta _g+V\) , and more generally fractional Schrödinger operators \(\Delta _g^\alpha +V\) , in the following setups: closed Riemannian manifolds, compact manifolds with boundary with suitable boundary condition, or even hyperbolic manifolds with infinite volume.
